My naive answer to this problem would be "well, then don't use a wire to hang them, use something that forces the frame against the wall". Which leaves you with

My naive answer to this problem would be "well, then don't use a wire to hang them, use something that forces the frame against the wall". Which leaves you with the issue that the frame might pull the nail out of the wall - but that also seems to be a solved problem: you can either use special picture hanging hooks which have up to 3 nails, with the nails angled upward so they won't be pulled out by a force facing downward. Or you can overengineer it and use a wall plug. This might not solve the author's problem, who seems to swap the pictures around often, but I assume most people don't do that...